4y^2-10y=3

Solution for 4y^2-10y=3 equation:

4y^2-10y=3

We move all terms to the left:

4y^2-10y-(3)=0

a = 4; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·4·(-3)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*4}=\frac{10-2\sqrt{37}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*4}=\frac{10+2\sqrt{37}}{8}
$